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A Novel Method to Estimate the System Dam** After Generator Trip**

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Abstract

Generator trip** strategies are generally decided by offline transient stability analysis. However, traditional methods can hardly ensure dynamic stability after GT. Simulation tests show that GT strategies change the topology and the state variables of a power system, which may weaken the system dam** after GT. In order to estimate the system dam**, this paper proposes a time-varying linearized model under unsteady states based on the virtual equilibrium point (VEP) theory. Then, the changes in dynamic characteristics caused by GT can be represented by the eigenvalues at VEPs before and after GT. An inertia equivalence system is mathematically formulated to analyze the effects of generator inertia, dam** ratio, and controllers. Two indices are designed to estimate the system dam** changes. Based on the indices, a framework is proposed to improve the current GT strategy decision-making system. The sensitivity analysis and the fault scanning verify the effectiveness and robustness of the proposed method and indices.

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Abbreviations

GT:

Generator trip**

EP:

Equilibrium point

VEP:

Virtual equilibrium point

LSM:

Least square method

COI:

Center of inertia

\(-\) :

The time before generator trip**

\(+\) :

The time after generator trip**

A:

Variables or parameters of COI A

B:

Variables or parameters of COI B

i :

Variables or parameters in cluster A

j :

Variables or parameters in cluster B

x :

Variables of the tripped generators

e :

Variables of the rest generators

\({\varvec{x}}\) :

State variables of generators

\(\varvec{\delta }\) :

Rotor angle of generators, rad

\(\omega\) :

Angular velocity of the rotor, rad/s

\({\omega }_{{\text{A}}}\) :

\(= \sum\nolimits_{{{i} \in {\text{cluster A}}}} {{\omega }_{{i}} {M}_{{i}} } /{M}_{{\text{A}}}\)

\(\varvec{\omega }_{{\text{B}}}\) :

\(= \sum\nolimits_{{{j} \in {\text{cluster A}}}} {{\omega }_{{j}} \varvec{M}_{{j}} } /{M}_{{\text{B}}}\)

\({\xi }\) :

Incoherence component of \({\omega }\)

\({\lambda }\) :

Eigenvalue of a matrix

\(\Delta {\sigma }\) :

Change of the real part of the critical eigenvalue

f :

A set of differential equations describing system dynamic characteristics

g :

A set of algebraic equations relating state and input variables to output variables

\({t}_{u}\) :

The time of fault clearing

\(t_{{\text{G}}}^{{}}\) :

The time of generator trip**

\({\varvec{A}}_{xx}\) :

\(= \partial {\varvec{f}}_{x} /\partial {\varvec{x}}_{x}\) in \(t_{{\text{G}}}^{ - }\), upper-left part of matrix

\({\varvec{A}}_{xe}\) :

\(= \partial {\varvec{f}}_{x} /\partial {\varvec{x}}_{e}\) in \(t_{{\text{G}}}^{ - }\), upper-right part of matrix

\({\varvec{A}}_{ex}\) :

\(= \partial {\varvec{f}}_{e} /\partial {\varvec{x}}_{x}\) in \(t_{{\text{G}}}^{ - }\), bottom-left part of matrix

\({\varvec{A}}_{ee}\) :

\(= \partial {\varvec{f}}_{e} /\partial {\varvec{x}}_{e}\) in \(t_{{\text{G}}}^{ - }\), bottom-right part of matrix

\({\varvec{A}}_{x}\) :

\(= \partial {\varvec{f}}_{x} /\partial {\varvec{x}}_{x}\) in \(t_{{\text{G}}}^{ - }\), diagonal part of state matrix

\({\varvec{A}}_{e}\) :

\(= \partial {\varvec{f}}_{e} /\partial {\varvec{x}}_{e}\) in \(t_{{\text{G}}}^{ - }\), diagonal part of state matrix

\({P}_{e}\) :

Electromagnetic power of generators

\({P}_{m}\) :

Mechanical power of generators

\({K}_{{{ij}}}\) :

\(= \partial {P}_{{{ei}}} /\partial {\delta }_{{j}}\)

\(\varvec{M}\) :

Inertia of generators

\({M}_{{\text{A}}}\) :

\(= \sum\nolimits_{{i \in \;{\text{cluster A}}}} {M_{i} }\)

\({M}_{{\text{B}}}\) :

\(= \sum\nolimits_{{j \in \;{\text{cluster B}}}} {M_{j} }\)

\(D\) :

Dam** ratio of generators

\(D_{{\text{A}}}\) :

\(= \sum\nolimits_{{i \in \;{\text{cluster A}}}} {D_{i} \omega _{i} \omega _{{\text{A}}} }\)

\(D_{{\text{B}}}\) :

\(= \sum\nolimits_{{j \in \;{\text{cluster B}}}} {D_{j} {\text{ }}\omega _{j} {\text{ }}\omega _{{\text{B}}} }\)

\({D}_{{{\Sigma A}}}\) :

\(= \sum\nolimits_{{i \in \;{\text{cluster A}}}} {D_{i} \;\omega _{i} }\)

\(\varvec{D}_{{{\Sigma B}}}\) :

\(= \sum\nolimits_{{i \in \;{\text{cluster B}}}} {D_{j} {\text{ }}\omega _{j} }\)

\(I_{C}\) :

Proposed index to assess the influence of the tripped generator

\(I_{D}\) :

Proposed index to estimate the changes of system dam**

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Acknowledgements

This work was supported by the fast analysis of cascading failures by integrating model-and data-driven methods Project (YKJ202108). We would like to especially thank ** Xu for coding the fundamental module of the method.

Funding

Nan**g Institute of Technology (CN), YKJ202108, Yun Liu.

Author information

Authors and Affiliations

  1. Electric Power Research Institute, State Grid Jiangsu Electric Power Co. Ltd, Nan**g, China

    Zi-Jun Bin, **n-Yao Zhu, **ang-** Kong & Ming-Shen Wang

  2. School of Electric Power Engineering, Nan**g Institute of Technology, Nan**g, China

    Yun Liu & Si-Peng Hao

Authors
  1. Zi-Jun Bin
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  2. Yun Liu
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  3. Si-Peng Hao
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  4. **n-Yao Zhu
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  5. **ang-** Kong
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Correspondence to Yun Liu.

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Appendix

Appendix

Fault scenario 2 is set to be a three-phase short-circuit in bus-27. The fault during time is 0.17 s. Fault scenario 3 is set to be a three-phase short-circuit in bus-27. The fault during time is 0.18 s, without GT control.

The critical clearing time of fault scenario 1 is 0.17 s. In other words, the system is transiently stable when the duration time of the fault is less than 0.17 s, as shown in Fig. 8.

Fig. 8
figure 8

Trajectories of rotor angles in fault scenario 2

Full size image

G9 and G5 are highlighted by blue and red curves, respectively.

Once the fault duration time is longer than 0.18 s, the system would lose transient stability in the first swing or the second swing, as shown in Fig. 9.

Fig. 9
figure 9

Trajectories of rotor angles in fault scenario 3

Full size image

G9 and G5 are highlighted by blue and red curves, respectively. Obviously, G9 is identified to be the critical generator. In the view of the current GT decision-making system, G9 would be chosen to trip.

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Bin, ZJ., Liu, Y., Hao, SP. et al. A Novel Method to Estimate the System Dam** After Generator Trip**. J. Electr. Eng. Technol. 18, 843–855 (2023). https://doi.org/10.1007/s42835-022-01261-6

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